Question

This circuit is equivalent to a single inductor having inductance $L_{eq}$ $=18H$ . Determine the value of the inductance $L$.

• A. $20H$
• B. $40H$
• C. $60H$
• D. $80H$

Answer 1

The correct option is A $20H$

The equivalent of 20H and 60H inductors connected in paralle is $\frac{20\times 60}{20+60}H=15H$

This is connected in series with $25H$ inductor giving an equivalent of $40H$.

Now this inductor is connected in parallel with $20H$ inductor and $L$, which are in turn connected to $10H$ inductor.

Hence, $L_{eq}=18H=10H+\frac{L\left(20\right)+L\left(40\right)+\left(20\right)\left(40\right)}{\mathrm{20.40.}L}$

$⟹L=20H$